Presence of a factor \(1/b\)  in above expression already indicates that a special care must be taken for \(b=0\)  case, which will be studied later in this article. The average steady state density of the system is \(\rho _s =\int _0^1 \mathrm {d}\rho \rho f(\rho )/\int _0^1\mathrm {d}\rho f(\rho ),\)  which can be calculated straightforwardly using the steepest-descent method [1]}; the resulting in
\(\rho _s =\begin{cases*}0 & d<0\\d & 0\le d<1 \& bd \le 1\\1 & otherwise\end{cases*}, \) 
